My attempts at clean fluid changes are always inadequate, and universally result in messes. I've also spilled plenty, trying to dump drain pans into jugs, trying to fill jugs from the fluid extractor, having wind catch the stream, dropping oil filters into pans. It's almost comical. Like others, I try to keep several pans, rags, and big pieces of cardboard available to catch as much mess as possible. And I learned the hard way, I never change oil in good clothes, no matter how "simple" it might be.
The worst: I was trying to use my fluid extractor and was unable to get more than 3 qts out. Figuring I'd have to replace the oil, so I could drive the vehicle onto ramps, I then tried reversing it to pump. The 2nd hose attachment was forced off during pumping, resulting in a geyser of oil I could not stop, so I literally had a oil hose spraying oil everywhere - on the engine, on the vehicle, on the ground... what a mess. What do you do with a pressurized oil geyser in your hand? (For those unaware, the best course is to open the air release value, to drop pressure.) It was worthy of a comedy skit. Several instances of fluid pumps or extractors going "rogue" and causing a mess.
Another time, I put my car on a lift, and was changing ATF but I miscalculated and positioned the tall catch pan too close. ATF sprayed out to the side overshooting the target by a foot. Put about 2 qts of ATF on the floor before I could react. Another time, I somehow managed to drive over my oil catch pan, destroying it. Thankfully it was mostly empty.